2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/26122The two dimensional Rashba Hamiltonian is investigated using the momentum representation.One finds that the SU(2) transformation which diagonalizes the Hamiltonian gives rise to non commuting Cartesian coordinates for K=0 and zero otherwise.This result corresponds to the Aharonov -Bohm phase in the momentum space. The Spin -Hall conductivity is given by $\frac{e}{4π}$ which disagree with the result $\frac{e}{8π}$ given in the literature.Using Stokes theorem we find that the Spin -Hall current is carried equally by the up and down electrons on the Fermi surface. We identify the Magnetic current and find that for an electric field with a finite Fourier component in the momentum space a non zero Spin -Hall current is obtained.For the electric field which is constant in space, the orbital magnetic current cancels the spin current. In order to measure the Spin-Hall conductance we propose to apply a magnetic field gradient $ΔH_{2}$ in the $i=2$ direction and to measure a Charge- Hall current $\frac{e}{h}(\frac{g}{2})μ_{B}ΔH_{2}$ in the $i=1$ direction.9 pages, 1 figure, submitted to PRLStrongly Correlated Electronstext